Let g（x） ∈L<sup>2</sup>（R） and （ω） be the Fourier transform of g（x）.Define g<sub>mn</sub>（x）=e<sup>imx</sup>g（x- 2πn）.In this paper we shall give a sufficient and nec...Let g（x） ∈L<sup>2</sup>（R） and （ω） be the Fourier transform of g（x）.Define g<sub>mn</sub>（x）=e<sup>imx</sup>g（x- 2πn）.In this paper we shall give a sufficient and necessary condition under which {g<sub>mn</sub>（x）} constitutes an orthonormal basis of L<sup>2</sup>（R） for compactly supported g（x） or （ω）.展开更多
基金This work is supported by the National Natural Science Foundation of China(No.19801005)the Project of New Stars of Science and Technology of Beijing a Grant of Young Fellow of Educational Ministry.
文摘Let g（x） ∈L<sup>2</sup>（R） and （ω） be the Fourier transform of g（x）.Define g<sub>mn</sub>（x）=e<sup>imx</sup>g（x- 2πn）.In this paper we shall give a sufficient and necessary condition under which {g<sub>mn</sub>（x）} constitutes an orthonormal basis of L<sup>2</sup>（R） for compactly supported g（x） or （ω）.
